# Circles (A_{1a}) and (A_{1b}): The Archimedean twins

The Adam and Eve of Archimedean circles in the arbelos.

Through C draw the perpendicular to AB, dividing the arbelos in two parts.
The incircles of these parts are congruent. [Archimedes]

### Properties

- The circular hull of the Archimedean twins has the same area as the arbelos
itself (and the circle with diameter CD). [Bankoff 1954]
- The common tangent of (A
_{1a}) with (O_{1}) passes through B, the common
tangent of (A_{1b}) and (O_{2}) passes through A. [Dodge e.a. 2000]
- The common tangent segment AT
_{b} is congruent to AD, the common tangent
segment BT_{a} is congruent to BD. [Dodge e.a. 2000]
- Let N
_{1} be the point where O_{1}A_{1a} meets CD then O_{1}N_{1} = O_{1}B. Let N_{2} be the
oint where O_{2}A_{1b} meets CD, then O_{2}N_{2} = O_{2}B.[Wendijk 2001/Hermann
2003, d'Ignazio and
Suppa 2001 - reworded]

Back to Catalogue

Home.